This invention relates to a process for the continuous, preparation of high-purity alkane sulfonic acid and/or alkane sulfonyl chloride in a reaction zone containing stationary (motionless and rigid) mixing elements which promote plug-flow. More particularly, it relates to a continuous process for the preparation of alkane sulfonic acid and/or alkane sulfonyl chloride product from a sulfur compound of the formula RSX where X is hydrogen or--SR.sup.1, and R and R.sup.1 are alkyl groups having from 1 to 20 carbon atoms, reacted with chlorine in an aqueous medium wherein the fluids of the reaction flow through a vertical reaction zone free of mechanical moving agitating means and containing stationary mixing elements which promote plug-flow, and continuously, separately withdrawing hydrochloride gas and product.